Use the disk or washer method to find the volume formed by rotating about the y-axis the region enclosed by:
x=4y and y^3=x with y>0
AAAaannndd the bot gets it wrong yet again!
The curves intersect at (0,0) and (8,2)
so, using shells of thickness dx,
v = ∫[0,8] 2πrh dx
where r = x and h= y^3-4y
v = ∫[0,8] 2πx(x^(1/^3)-x/4) dx = 512π/21
using discs of thickness dy, we have
v = ∫[0,2] π(R^2-r^2) dy
where R = 4y and r = y^3
v = ∫[0,2] π((4y)^2-(y^3)^2) dy = 512π/21
Volume = π ∫[0,4] (4y)^2 dy
= π ∫[0,4] 16y^2 dy
= π [8y^3/3] |[0,4]
= π (8*64/3)
= 1024π/3